
where \(\rho _0 \triangleq P \sigma _h^2/N_0\) , \(\Gamma _{\text{inc}} (s,x) = \int _x^{\infty } t^{s-1}\,e^{-t}\,{\rm d}t\)  is the upper incomplete gamma function and \(\Gamma (s)\)  is the ordinary gamma function.
The interference is written as \(t_{mi} = |\mathbf {h}_m^H \mathbf {h}_i|^2/(\Vert \mathbf {h}_m\Vert ^2 \Vert \mathbf {h}_i\Vert ^2)\) , where \(t_{mi} \sim \text{Beta}(\alpha = 1, \beta = N)\) .
We have \(\Vert \mathbf {h}_i\Vert ^2/N \stackrel{\text{a.s.}}{\longrightarrow } \sigma _h^2\)  and \(\Vert \mathbf {h}_i\Vert ^4/N^2 \stackrel{\text{a.s.}}{\longrightarrow } \sigma _h^4\)  as \(N \rightarrow \infty \)  [1]}.
Thus, we can approximate the SINR as
\({\rho }_m^k&\approx N(\rho _0^{-1}+ N\textstyle {\sum _{i \in \mathcal {S}_k^m}} t_{mi})^{-1}.\) 
